Domains of quantification

What kind of domains do generalized quantifiers quantify over? The traditional domain is that of individuals, and that is what the present book focuses on, but the same basic ideas and techniques extend to other domains, such as times and (indices of) possible worlds, and higher-order entities. Beyond its linguistic interest, this fact has some philosophical interest as well: Quine (1948) famously (and controversially) proposed that “To be is to be the value of a variable”. The present section offers some pointers to the literature on various domains of quantification; §3.2 shows that the methods of scope assignment reviewed in Chapter 2 in connection with nominal quantifiers carry over to a new kind of expression: raising verbs.

Linguists and philosophers have argued that the domain of first-order entities is articulated into different sorts: alongside tangible individuals like people and books we have kinds (Carlson 1977), sums (Link 1983), individual correlates of properties (Chierchia 1984), events (Davidson 1967; Krifka 1989; Schein 1993; Lasersohn 1995; de Swart 1993; Borer 2005a,b), and more recently degrees or intervals of degrees (Kennedy 1999; Schwarzschild and Wilkinson 2002; Heim 2001, 2006a). Two other domains are moments or intervals of time, and possible worlds and parts thereof: situations (Hintikka 1962; Bennett and Partee 1972/2002; Cresswell 1990; Heim 1992; von Stechow 2003, 2004; Kratzer 1989, 2002; Kusumoto 2005).

Contemplating the cross-linguistic division of labor at the syntax/semantics interface Partee (1991) distinguishes D(eterminer)-quantification from A-quantification, where A stands for “the cluster of Adverbs, Auxiliaries, Affixes, and Argument-structure Adjusters”.